Elastocapillary Deformation of Soft Matter Beams on Elastic Substrate
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摘要: 当软物质微/纳米结构表面存在液滴时，需要考虑由润湿诱导的弹性毛细变形. 该文基于一个新的润湿方程，推导了液滴铺展半径与其表面曲率的关系，并得到了无重力影响时液滴保持球冠状的必要条件；结合Winkler地基模型，计算了弹性基底上软物质微梁的弹性毛细变形，得到了微梁挠度的解析解. 以聚苯乙烯(EPS)和聚乙烯(PE)梁为例，分析并讨论了液滴铺展半径、弹性模量和基底参数对微梁的挠曲变形以及从基底上脱黏的影响.
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关键词:
- 润湿 /
- 弹性毛细变形 /
- Winkler地基模型 /
- 软物质 /
- 微梁
Abstract: With droplets on the surface of soft matter or micro/nanostructures, wetting-induced elastocapillary deformation should be considered. Based on a new wetting equation, the relationship between the droplet spreading radius and its surface curvature was determined, and the necessary conditions for the droplet to hold the spherical cap without the influence of gravity were obtained. Combined with the Winkler foundation model, the elastocapillary deformation of soft material microbeam on elastic substrate was calculated. The analytical solution for the deflection of the microbeam was given. With polystyrene and polyethylene beams as examples, the influences of the droplet spreading radius, the beam material elastic modulus and the Winkler foundation parameter on the microbeam deflections and detachments from the substrate, were analyzed and discussed.-
Key words:
- wetting /
- elastocapillary deformation /
- Winkler foundation model /
- soft matter /
- microbeam
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图 2 润湿引起弹性基底上梁的变形
Figure 2. Wetting induced deformation of a beam on elastic foundation
图 4 液滴半径R=0.01 mm，0~l1段梁所受合力f(l1)
Figure 4. For droplet radius R=0.01 mm, resultant force f(l1) of the beam in the 0~l1 section
图 6 半径为1 mm的液滴润湿导致的微梁弯曲
Figure 6. The deflection curve of the micro-beam wetted by a droplet with a radius of 1 mm
图 7 半径为0.1 mm的液滴润湿导致的微梁弯曲
Figure 7. The deflection curve of the micro-beam wetted by a droplet with a radius of 0.1 mm
图 8 半径为0.01 mm的液滴润湿导致的微梁弯曲
Figure 8. The deflection curve of the micro-beam wetted by a droplet with a radius of 0.01 mm
图 9 PE和EPS微梁在半径为0.01 mm液滴作用下的弹性毛细弯曲
Figure 9. Elastocapillary bending of PE and EPS microbeams subjected to droplet action with a radius of 0.01 mm
图 10 不同弹性基底上的液滴引起的微梁的弯曲变形(R=0.01 mm)
Figure 10. Deflection curves of microbeams caused by droplets on different elastic substrates (R=0.01 mm)
表 1 EPS微梁的材料参数与几何参数
Table 1. Material and geometric parameters of the EPS micro-beam
l/mm E/MPa d/mm h/mm I/mm4 5 1.8 1 0.05 1/96 000 
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表 2 微梁最大挠度及黏附长度与液滴半径的对应关系
Table 2. Maximum deflections and adhesive lengths of the micro-beam vs. droplet radii
parameter R/mm 1 0.1 0.01 y(0)/mm 0.024 2 0.046 2 0.049 6 l1/mm 1.4 0.83 0.82
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表 3 微梁的最大挠度及黏附长度随基床系数的变化
Table 3. Maximum deflections and adhesive lengths of the micro-beam vs. the bedding coefficient
parameter k/(10-3·N/mm3) 1 1.5 2 20 y(0)/mm 0.046 1 0.034 0 0.027 4 0.004 9 l1/mm 2.60 2.35 2.19 1.23
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